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Chapter 4: Q7DQ (page 911)

A charged particle moves through a region of space with constant velocity (magnitude and direction). If the external magnetic field is zero in this region, can you conclude that the external electric field in the region is also zero? Explain. (By 鈥渆xternal鈥� we mean fields other than those produced by the charged particle.) If the external electric field is zero in the region, can you conclude that the external magnetic field in the region is also zero?

Short Answer

Expert verified

We can conclude that the electric field also equals zero. We cannot make a conclusion concerning whether the magnetic field is also zero in this case.

Step by step solution

01

Definition of Lorentz force

The force exerted on a charged particle q moving with velocity v through an electric field E and magnetic field B. The entire electromagnetic force F on the charged particle is called Lorentz force and is given byF鈫�=q(E鈫�+v鈫�脳B鈫�)

02

Determine if magnetic field is zero, whether electric field is also zero

The particle will move in the described way only if

F鈫�=0鈫�

If B鈫�=0鈫�, thenB鈫�=qE鈫�=0

which is possible only ifE鈫�=0鈫�

Hence, we can conclude that the electric field is also zero.

03

Determine if electric field is zero, whether magnetic field is also zero

If E鈫�=0鈫�, thenF鈫�=qv鈫�脳B鈫�=0鈫�

and this can happen ifB鈫�=0鈫� or when is perpendicular to v鈫�.

Hence, we cannot make a conclusion concerning whether magnetic field is also zero in this case.

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